A non astringent cultivar, such as FUYU can be eaten like an apple(before it softens) or afterwards when it fully softens and ripens. Astringent cultivars can only be eaten after they soften and tannin levels drop. They often have much richer flavors than a ripe FUYU.
Other main differences between cultivars would be shape, size, flesh color (orange, red, cinnamon, brown ) seedyness, drying ability etc.
Astringent cultivars may be more critter resistant ?
Seedless non astringent types are popular with growers, as they are easier to market/export. Ripe astringents can be very messy !